/*
 * Median of Two Sorted Arrays
 * 
 * There are two sorted arrays A and B of size m and n respectively. 
 * Find the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)).
 */ 

//The simplest way is merging the two sorted array, then get the median. In that case, run time is 0(m+n).
#include <iostream>
#include <algorithm>

using namespace std;

double findKth(int a[], int m, int b[], int n, int k)
{
	//always assume that m is equal or smaller than n
	if (m > n)
		return findKth(b, n, a, m, k);
	if (m == 0)
		return b[k - 1];
	if (k == 1)
		return min(a[0], b[0]);
        
	//divide k into two parts
	int pa = min(k / 2, m), pb = k - pa; //分割数组是关键 每次循环排除pa个元素
        //int pa = max(1,m/2), pb = k - pa;  ／／小狗分割法，不好。。。收敛速度不快。。。大测试过不了
	if (a[pa - 1] < b[pb - 1])
		return findKth(a + pa, m - pa, b, n, k - pa);
	else if (a[pa - 1] > b[pb - 1])
		return findKth(a, m, b + pb, n - pb, k - pb);
	else
		return a[pa - 1];
}

double findMedianSortedArrays(int A[], int m, int B[], int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
    int total = m + n;
		if (total & 0x1) //odd
			return findKth(A, m, B, n, total / 2 + 1);
		else
			return (findKth(A, m, B, n, total / 2)
					+ findKth(A, m, B, n, total / 2 + 1)) / 2;
    
    }

void TestfindMedianSortedArrays()
{
    int A[]={2};
    int B[]={1};
    double median = findMedianSortedArrays(A,1,B,1);
    cout<<"Median:"<<median;
}
